Question

Use the image to answer the question.

An illustration shows a scatterplot titled Attendance. The x-axis shows days ranging from 0 through 110 in increments of ten. The y-axis shows number of patrons and ranges from 600 to 800 in 25 unit increments.
Ten points are plotted on the graph. A kink is shown on both the x- and y-axes close to the origin to indicate a break in the data. The points are plotted at approximate coordinates left parenthesis 10 comma 725 right parenthesis, left parenthesis 20 comma 675 right parenthesis, left parenthesis 30 comma 700 right parenthesis, left parenthesis 40 comma 750 right parenthesis, left parenthesis 50 comma 650 right parenthesis, left parenthesis 60 comma 675 right parenthesis, left parenthesis 70 comma 700 right parenthesis, left parenthesis 80 comma 725 right parenthesis, left parenthesis 90 comma 725 right parenthesis, and left parenthesis 100 comma 650 right parenthesis.

A petting zoo graphed the average attendance of patrons every 10 days over a 100 day period of time. Interpret the scatterplot to determine what type of association the scatterplot shows.

(1 point)
Responses

The graph is non-linear.
The graph is non-linear.

The graph shows a linear association.
The graph shows a linear association.

The graph shows a negative association.
The graph shows a negative association.

The graph shows a positive association.
The graph shows a positive association.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The graph shows a slight non-linear association, as the points do not form a perfectly straight line. However, there is a general trend of increasing attendance as the number of days increases. Therefore, the scatterplot shows a positive association.

Answer 2

Interpret the scatterplot to determine what type of association the scatterplot shows.

(1 point)
Responses

linear association
linear association

non-linear association
non-linear association

no association
no association

negative association

Answer 3

[AI-generated answer — Bot GPT 3.5]

The scatterplot shows a non-linear association.

Answer 4

Use the table to create a scatterplot. Determine the type of association.

x
25 30 80 150 250 350 425 450 500
y
375 225 120 75 50 100 175 275 400


(1 point)
Responses

negative linear association
negative linear association

non-linear association
non-linear association

linear association
linear association

no association
no association

Answer 5

[AI-generated answer — Bot GPT 3.5]

To create a scatterplot based on the table:

x: 25, y: 375
x: 30, y: 225
x: 80, y: 120
x: 150, y: 75
x: 250, y: 50
x: 350, y: 100
x: 425, y: 175
x: 450, y: 275
x: 500, y: 400

After plotting these points and looking at the scatterplot, it appears that the points do not form a straight line, which indicates a non-linear association.

Answer 6

Use the image to answer the question.

An illustration of a scatterplot shows x on x-axis from 65 to 75 in increments of 1 and y on the y-axis from 200 to 240 in increments of 2.5. Eleven points are plotted. The approximate plotted points are as follows: left parenthesis 65 comma 205 right parenthesis, left parenthesis 67 comma 216 right parenthesis, left parenthesis 68 comma 210 right parenthesis, left parenthesis 68 comma 218 right parenthesis, left parenthesis 69 comma 224 right parenthesis, left parenthesis 70 comma 220 right parenthesis, left parenthesis 70 comma 224 right parenthesis, left parenthesis 71 comma 230 right parenthesis, left parenthesis 72 comma 235 right parenthesis, left parenthesis 74 comma 200 right parenthesis, and left parenthesis 74 comma 240 right parenthesis.

Is there a relationship between the two sets of data? Choose 1 for yes and 2 for no.

(1 point)

Answer 7

[AI-generated answer — Bot GPT 3.5]

1. Yes, there is a relationship between the two sets of data.

Answer 8

Question

Use the image to answer the question.

An illustration of a scatterplot graph is titled Animal Longevity. It shows x-axis, labeled as average, ranging from 0 to 45 in increments of 5 and y-axis, labeled as maximum, ranging from 0 to 80 in increments of 10.
Multiple points are plotted around a line that points upward to the right with an arrowhead on the top. The line passes approximately through left parenthesis 0 comma 20 right parenthesis, left parenthesis 15 comma 40 right parenthesis, left parenthesis 30 comma 60 right parenthesis, and left parenthesis 40 comma 78 right parenthesis. Two dotted lines are drawn forming a triangle under the line with the line being the hypotenuse. The dotted lines are drawn from left parenthesis 15 comma 40 right parenthesis to left parenthesis 30 comma 40 right parenthesis and from left parenthesis 30 comma 60 right parenthesis to left parenthesis 30 comma 40 right parenthesis. 8 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
y=

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the equation of the trend line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) using two points on the line. Let's take the points (0, 20) and (40, 78).

slope (m) = (y2 - y1) / (x2 - x1)
m = (78 - 20) / (40 - 0)
m = 58 / 40
m = 1.45

Now that we have the slope, we can find the y-intercept (b) by substituting one of the points into the slope-intercept equation. Let's use the point (15, 40):

40 = 1.45(15) + b
40 = 21.75 + b
b = 40 - 21.75
b = 18.25

Therefore, the equation of the trend line in slope-intercept form is:
y = 1.45x + 18.25

Answer 10

Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 15 in increments of 1 and y-axis ranging from 0 to 75 in increments of 5. Multiple points are plotted and a line points upward to the right with an arrowhead on the top.
The line passes approximately through left parenthesis 0 comma 25 right parenthesis, left parenthesis 1 comma 30 right parenthesis, left parenthesis 2 comma 35 right parenthesis, left parenthesis 7 comma 60 right parenthesis, and left parenthesis 10 comma 75 right parenthesis. 5 points are plotted to the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
y=

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the equation of the trend line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) using two points on the line. Let's take the points (0, 25) and (10, 75) since these are the endpoints of the line.

slope (m) = (y2 - y1) / (x2 - x1)
m = (75 - 25) / (10 - 0)
m = 50 / 10
m = 5

Now that we have the slope, we can find the y-intercept (b) by substituting one of the points into the slope-intercept equation. Let's use the point (0, 25):

25 = 5(0) + b
b = 25

Therefore, the equation of the trend line in slope-intercept form is:
y = 5x + 25.

Answer 12

Use the image to answer the question.

An illustration shows the first quadrant of a coordinate plane titled Chapters of a Books versus pages. The x-axis shows chapters and ranges from 0 to 20 in increments of 1. The y-axis shows pages and ranges from 0 to 220 in increments of 20.
Ten points are plotted on the graph. The points are plotted at approximate coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma 20 right parenthesis, left parenthesis 4 comma 45 right parenthesis, left parenthesis 5 comma 50 right parenthesis, left parenthesis 8 comma 95 right parenthesis, left parenthesis 10 comma 90 right parenthesis, left parenthesis 12 comma 130 right parenthesis, left parenthesis 17 comma 170 right parenthesis, left parenthesis 18 comma 160 right parenthesis, and left parenthesis 20 comma 210 right parenthesis. An upward slanting line starts at left parenthesis 0 comma 0 right parenthesis and continues to left parenthesis 17 comma 170 right parenthesis.

A librarian collected data on the number of pages in chapters of a book. Interpret the slope and the y-intercept of the linear model. Round the slope to the nearest hundredth.

(1 point)
Responses

For every chapter of a book, there is an average of 0.1 page.
For every chapter of a book, there is an average of 0.1 page.

For every 10 chapters of a book, there is an average of 1 page.
For every 10 chapters of a book, there is an average of 1 page.

For every chapter of a book, there is an average of 10 pages.
For every chapter of a book, there is an average of 10 pages.

For every chapter of a book, there is an average of110 page.

Answer 13

[AI-generated answer — Bot GPT 3.5]

To interpret the slope and y-intercept of the linear model, we first need to determine the values using the points provided.

Let's use the points (0, 0) and (17, 170) to find the slope (m):
m = (170 - 0) / (17 - 0)
m = 170 / 17
m = 10

Now, let's find the y-intercept (b) using the slope and one of the points (0, 0):
y = mx + b
0 = 10(0) + b
b = 0

Therefore, the slope of the linear model is 10, indicating that for every 1 chapter, on average, there are 10 pages. The y-intercept is 0, meaning that the book starts with 0 pages at chapter 0.

The closest answer option provided is:
"For every 10 chapters of a book, there is an average of 1 page." - This is not accurate in this case as the correct interpretation is the slope being 10, indicating that for every chapter, there are an average of 10 pages.

Answer 14

Use the image to answer the question.

A veterinarian collected data on the average weight of dogs by age in months. Interpret the slope and the y-intercept (0,0) of the linear model, using the ordered pair (9,42). Round the slope to the nearest hundredth.

(1 point)
Responses

Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth.
Every month, a dog averages a gain of 0.21 pounds and weighs 0 pounds at birth.

Every month, a dog averages a gain of 4.67 pounds
Every month, a dog averages a gain of 4.67 pounds

Every 4.67 months, a dog averages a gain of 1 pound and weighs 0 pounds at birth.
Every 4.67 months, a dog averages a gain of 1 pound and weighs 0 pounds at birth.

Every month, a dog averages a gain of 4.3 pounds and weighs 0 pounds at birth.

Answer 15

[AI-generated answer — Bot GPT 3.5]

To interpret the slope and y-intercept using the point (9, 42), we can calculate the slope (m) and y-intercept (b) of the linear model.

Given one point (0, 0) and the point (9, 42):
m = (42 - 0) / (9 - 0)
m = 42 / 9
m = 4.67 (rounded to the nearest hundredth)

Using the point (0, 0):
0 = 4.67(0) + b
b = 0

Therefore, the slope of the linear model is 4.67, indicating that on average, a dog gains approximately 4.67 pounds per month. The y-intercept is 0, suggesting that a dog has an estimated starting weight of 0 pounds at birth.

The answer that correctly interprets the slope and y-intercept is:
"Every month, a dog averages a gain of 4.67 pounds and weighs 0 pounds at birth."

Answer 16

Use the image to answer the question.

A scatterplot on a coordinate plane of quadrant 1 is titled as Snow Accumulation in Inches per Hour.
"The plane shows the x-axis, labeled as Hours, ranging from 0 to 6 in increments of 1, and the y-axis, labeled as Snow Accumulation in Inches, ranging from 0 to 12 in increments of 1. Six points are plotted and an upward line is drawn through or near the points. The line passes approximately through the following unlabeled points: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 1.5 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 3 comma 5 right parenthesis, left parenthesis 4 comma 7.5 right parenthesis, and left parenthesis 6 comma 10 right parenthesis."

A meteorologist collected data on a recent snowfall. The meteorologist graphed the data and found the equation of the trend line to be y=1.7x+0.1 . If the snowfall continues at this pace, use the equation to predict the number of inches of snow after 10 hours. Round to the nearest tenth.

(1 point)
After 10 hours, the snowfall would be
inches.

Answer 17

[AI-generated answer — Bot GPT 3.5]

To predict the number of inches of snow after 10 hours using the given equation y = 1.7x + 0.1, where x represents the number of hours:

Substitute x = 10 into the equation:
y = 1.7(10) + 0.1
y = 17 + 0.1
y = 17.1

After 10 hours, the predicted snow accumulation would be approximately 17.1 inches.

Answer 18

Use the table to answer the question.

Apples Banana Oranges Totals
7th graders 44 120
8th graders 35 46
Totals 72 71
Constructing the two-way table, what is the total number of seventh graders who prefer bananas?

(1 point)
Responses

25
25

86
86

69
69

51

Answer 19

[AI-generated answer — Bot GPT 3.5]

To find the total number of seventh graders who prefer bananas, we look at the given data in the table:

7th graders who prefer apples = 44
7th graders who prefer oranges = 120 - 44 = 76 (from the total given)
Total number of 7th graders = 120

Thus, to find the number of 7th graders who prefer bananas:
7th graders who prefer bananas = Total 7th graders - (7th graders who prefer apples + 7th graders who prefer oranges)
7th graders who prefer bananas = 120 - (44 + 76)
7th graders who prefer bananas = 120 - 120
7th graders who prefer bananas = 0

Therefore, the total number of seventh graders who prefer bananas is 0.

Answer 20

Use the table to answer the question.

Age For Against No Opinion
21–30 40 22 18
31–40 30 50 25
Over 40 25 35 8
A poll was taken to explore the relationship between age and support for a candidate in an election. The results of the poll are summarized in the table. How many people above age 30 are for the candidate?

(1 point)
Responses

95
95

70
70

55
55

40

Answer 21

[AI-generated answer — Bot GPT 3.5]

To find the number of people above age 30 who support the candidate, we add the number of people that are in the "For" category for the age groups 31-40 and Over 40.

For age 31-40: 30 people are for the candidate
For age Over 40: 25 people are for the candidate

Total number of people above age 30 who support the candidate:
30 (age 31-40) + 25 (Over 40) = 55

Therefore, there are 55 people above age 30 who are for the candidate.

Answer 22

Use the table to answer the question.

Preference 7th Graders 8th Graders
Prefers Cats 36 22
Prefers Dogs 8 26
No Preference 2 6
What is the relative frequency of students who prefer dogs who are 7th graders? Round the percentage to the nearest tenth.

(1 point)
Responses

8%
8%

76.5%
76.5%

17.4%
17.4%

23.5%

Answer 23

[AI-generated answer — Bot GPT 3.5]

To find the relative frequency of 7th graders who prefer dogs, we need to look at the total number of 7th graders who prefer dogs and divide it by the total number of students in 7th grade.

Total number of 7th graders who prefer dogs = 8
Total number of 7th graders = 36 (prefers cats) + 8 (prefers dogs) + 2 (no preference) = 46

Relative frequency of 7th graders who prefer dogs:
(8 / 46) * 100 = 17.4%

Therefore, the relative frequency of 7th graders who prefer dogs is 17.4%.

Answer 24

Use the table to answer the question.

Hip-Hop Pop Totals
10th Grade 112 53 165
11th Grade 98 147 245
Total 210 200 410
Examine the data from a survey of 10th and 11th graders about which music genre they prefer.

Using relative frequencies, which of the following is true?

(1 point)
Responses

If you are a 10th grader, you are more likely to prefer pop.
If you are a 10th grader, you are more likely to prefer pop.

If you are an 11th grader, you are more likely to prefer hip-hop.
If you are an 11th grader, you are more likely to prefer hip-hop.

If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

If you like pop, you are more likely to be a 10th grader.

Answer 25

[AI-generated answer — Bot GPT 3.5]

To determine which statement is true using relative frequencies:

For 10th graders:
- The relative frequency of 10th graders who prefer Hip-Hop: 112 / 165 ≈ 0.6788
- The relative frequency of 10th graders who prefer Pop: 53 / 165 ≈ 0.3212

For 11th graders:
- The relative frequency of 11th graders who prefer Hip-Hop: 98 / 245 ≈ 0.4
- The relative frequency of 11th graders who prefer Pop: 147 / 245 ≈ 0.6

Comparing the relative frequencies:

- If you are a 10th grader, you are more likely to prefer Hip-Hop.
- If you are an 11th grader, you are more likely to prefer Pop.
- If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
- If you like pop, you are more likely to be an 11th grader.

Therefore, the statement "If you are a 10th grader, you are more likely to prefer Hip-Hop" is true based on the given data.

Answer 26

Use the image to answer the question.

A scatterplot shows the number of cups of coffee sold versus temperature.
The horizontal axis shows temperature, in degrees Fahrenheit, ranging from 0 to 70 in increments of 5, with an initial jump from 0 to 25. The vertical axis shows number of cups of coffee sold, ranging from 0 to 60 in increments of 10. A kink is shown on the horizontal axis close to origin. A tightly packed cluster of data plots is plotted between 30 to 37 on the horizontal axis and 42 to 48 on the vertical axis. A loosely packed cluster of data plots is plotted between 40 to 51 on the horizontal axis 30 and 38 on the vertical axis and. A dot is plotted at 62 on the horizontal axis and 5 on the vertical axis.
Numbers of Cups of Coffee Sold Versus Temperature

Interpret the scatterplot by describing any outliers and patterns of clustering.

(4 points)

Answer 27

[AI-generated answer — Bot GPT 3.5]

In interpreting the scatterplot of the number of cups of coffee sold versus temperature, we observe the following:

1. Outliers:
- The point plotted at 62 degrees Fahrenheit and 5 cups sold seems to be an outlier as it is significantly distant from the other data points, indicating an unusual observation compared to the main cluster of data.

2. Clustering Patterns:
- There is a tightly packed cluster of data points between 30 to 37 degrees Fahrenheit and 42 to 48 cups of coffee sold. This cluster suggests a consistent trend where the number of cups sold tends to be higher within this temperature range.
- Additionally, there is a loosely packed cluster of data points between 40 to 51 degrees Fahrenheit and 30 to 38 cups of coffee sold. This indicates a less consistent pattern compared to the tighter cluster, showing more variability in the number of cups sold within this temperature range.

Overall, the scatterplot indicates a general positive correlation between temperature and the number of cups of coffee sold. The outliers and clustering patterns help in understanding the relationship between temperature and coffee sales.